Hi my friends

i'm studying Transfer function T(s) subject ,, i faced problem with the question and i had tried to solve it as attached photo

Please help me and thanks in advance,,

 

You seem to have invented a new Laplace transform pair, namely that the Transform of the ratio of two functions is the ratio of the transforms of the two functions. Believe that?

You need to follow the process step by step.

Y(s) = H(s)R(s)

So, given r(t), find R(s). Don't forget the implication of using the one-sided Laplace transform!

Then find Y(s).

Then find y(t) by taking the inverse transform of Y(s).

 

You seem to have invented a new Laplace transform pair, namely that the Transform of the ratio of two functions is the ratio of the transforms of the two functions. Believe that?

You need to follow the process step by step.

Y(s) = H(s)R(s)

So, given r(t), find R(s). Don't forget the implication of using the one-sided Laplace transform!

Then find Y(s).

Then find y(t) by taking the inverse transform of Y(s).

Really really thanks u sooooooooo much for your help
I am getting correct answer when i applied your steps correctly as attached photo

 

Good!

While it doesn't affect your answer to this problem (since you are looking for the value at a specific time greater than zero), your y(t) is not quite correct. What is y(t) for t=-1sec? According to your answer it is 45 when it should be 0. Again, the implication of working with the one-sided function is that your inputs and outputs are one sided. So you need to multiply your result by u(t).